Wuhaib, Sufyan Abaas
(2013)
Dynamics Of Predator-Prey Models.
PhD thesis, Universiti Sains Malaysia.
Abstract
In this thesis, we studied a number of predator prey system involving factors such as infections,
harvesting, phase structure, constant and random refuges and frequent encounters of predator
and prey. Through analysis and comparison we found the effect of the infection on the existence
and the stability of populations systems; this stability may turn into instability and sometimes
into simple Hopf bifurcation. It was also found that harvesting does not affect the existence
and stability of systems, but affects the disease, and thus can be used to control the disease, tak-
ing into account that excessive harvesting may lead to extinction of communities. We employ
the basic reproduction number to construct regions, whereby in these regions all populations
survive, disease under control and the continuation of the harvest guaranteed. We propose an
optimal harvest policy in that the harvest begins in the initial stages of the presence of disease
and this ensures the disease is under control and prevent it from spreading. Another factor
affecting disease is the stage structure of the predator. In this model, the prey becomes infected
while the predator is divided into two groups, mature and immature. When the disease disap-
pears, the model consists of susceptible prey, immature and mature predator and this model is
stable. The prey sometimes uses places to escape from the predator and these places are called
refuges. The refuges affect the stability of the models and the existence of populations. We
studied constant and random refuges to show that the constant refuges are better than random
refuges; they are more stable and offer a better chance of survival than random refuges. We
next study models of the food chain.
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